Abstract
Let X be a non-empty set. We say that an element x is an element of X is a phi-fixed point of T, where phi : X -> [0, infinity) and T : X -> X, if x is a fixed point of T and phi : (x) = 0. In this paper, we establish some existence results of.-fixed points for various classes of operators in the case, where X is endowed with a metric d. The obtained results are used to deduce some fixed point theorems in the case where X is endowed with a partial metric p.